Logarithm Rules, Tables, Formulas and Shortcuts

Logarithm Solved Examples - Page 3
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Logarithm, in mathematics is the exponent or power to which a stated number called base , is raised to yield a specific number. For example on the expression 10^{2}\, =\, 100 , the Logarithm of 100 to the base 10 is 2. This is written as Log_{10}\, 100\, =\, 2 Logarithms were originally invented to help simplify the arithmetical processes of multiplication, division, expansion to a power and extraction of a 'root', but they are now a days used for variety of purposes in pure and applied mathematics.

If for a positive real number (a ≠ 1) , a^{m}\, =\, b , then the index m is called the Logarithm of b to the base a.
We write this as: Log_{a}b\, m
Log begins the abbreviation of the word ‘Logarithm’. Thus a^{m}\, b\, \leftrightarrow \, log_{a}b\, =\, m
Where a^{m} = b is called the exponential form and Log_{a}b\, =\, m is called the Logarithmic form.

Exponential Form
3^{5}\, =\, 243
2^{4}\, =\, 16
3^{0}\, =\, 1
8^{\frac{1}{3}}\, =\, 2

Logarithmic Form

log_{3}243\, =\, 5
log_{2}16\, =\, 4
log_{3}1\, =\, 0
log_{8}2\, =\, \frac{1}{3}

 

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